Time-optimal solar sail heteroclinic-like connections for an Earth-Mars cycler

Abstract

This paper investigates solar sail Earth-Mars cyclers, in particular cyclers between libration point orbits at the Earth-Moon L2 point and the Sun-Mars L1 point. In order to facilitate cyclers in as few Earth-Mars synodic periods as possible, the overall objective is to minimize the time of flight. These time-optimal cyclers are obtained by using a direct pseudospectral method and exploiting techniques from dynamical systems theory to obtain an initial guess. In particular, heteroclinic connections between the unstable and stable manifolds of the target libration point orbits at the Earth-Moon L2 point and the Sun-Mars L1 point are sought for. While such connections do not exist in the ballistic case, they can be achieved by complementing the dynamics with a solar sail and assuming a constant attitude of the sail with respect to the direction of sunlight. These trajectories are sub-optimal due to the assumed constant sail attitude as well as minor discontinuities in position and velocity at the linkage of the manifolds, which are overcome by transferring the initial guess to the direct pseudospectral optimal control solver. For near- to mid-term sails, results show time-optimal round-trip trajectories that span three synodic Earth-Mars periods, with a few months to one year stay times at the libration point orbits, depending on the time of departure within a five-month window. Through the propellant-less nature of solar sailing, these Earth-Mars cyclers can, in theory, be maintained indefinitely.